An Illustration of the Duality Technique in Semi-Continuous Linear Programming

We give a complete parametric solution of the following problem. Find a claim size distribution F on the finite interval [o,w], maximizing the stop-loss premium corresponding to a given excess e, under the constraints that the first moment of F be at most equal to u and the second at most equal to v. The method used is the duality technique in semi-continuous linear programming described in De Vylder (1978). This technique is summarized, without proofs, in the first part of the paper.